Good news, now it's OK !
I don't really know why, but I had to declare the characteristics as "BLERead | BLEWrite" and to use a sequence : WriteStringsWithResponse + ReadStrings instead of WriteStrings.
Here is my new block sequence :
Notice another error that I fund : The WriteByteWithResponse of "13" value +ReadBytes sequences shall be done at the end, after having broadcasted the Strings (if not, the "updateBio()" subprogram is launched before update of strings).
Hope it will helps other people having some trouble with strings.
Regards
Thomas